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| DR. JOHN RASP'S STATISTICS WEBSITE |
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STAT 301 - Business Statistics Answer the following questions. Remember to show work on the computational exercises. (You do not need to work out the standard deviations by hand — use Excel’s built-in function. You should be able to do standard deviations by hand for simple sets of "nice" numbers — but the data in these problems go beyond that.) Review questions: 1) What is Student's t distribution? When is it used? 2) When do we use a confidence interval in statistical inference? A hypothesis test? Computational exercises: 1) The Financial Aid office at the University of Southern North Dakota at Hoople wishes to estimate the amount of money the average student spends on textbooks. (They plan to use the result to help them determine a student's financial need, and to plan financial aid awards.) They randomly select students. They then contact the university registrar to obtain each student's course schedule for the semester. Next they visit the campus bookstore to determine what books are required for these classes, and to obtain the cost of the necessary textbooks. The total textbook costs for the ten students are as follows:
a) Find a 95% confidence interval for the (population) mean cost of textbooks. b) What would the Financial Aid office need to do, to reduce the width of their confidence interval? c) Note that the Financial Aid office did not take a survey to obtain data. What are the relative advantages and disadvantages of obtaining data the way they did? 2) The Sirius Cybernetics Corporation wishes to estimate mean time-to-failure for one of its new products, a solar powered flashlight. (They need this information so they can determine the product warranty appropriately.) They test twenty flashlights. Their (sample) mean time to failure is 846 hours, with a standard deviation of 42 hours. a) Find a 95% confidence interval for the (population) mean time to failure. b) Why is it inappropriate to find a 95% confidence interval for the sample mean time to failure? c) Realistically, Sirius Cybernetics is not only interested in mean time to failure. Since they're using the data to establish a product warranty, one of the questions they would like to answer is: What do we establish as the warranty time so that virtually all the flashlights last longer than that? If flashlight lifelengths are normally distributed, how long should the warranty be? d) How would you tell whether the "normally distributed" assumption in Part C holds? 3) A builder has contracted for the delivery of 400,000 pounds of fill dirt. The supplier proposes making delivery in 100 truckloads that he claims will average 4000 pounds. The builder insists on weighing a random sample of 16 truckloads and obtains these data:
(I took these data from Gary Smith's book, Statistical Reasoning.) Use these data to conduct an appropriate hypothesis test. 4) Compute a 95% confidence interval for the mean truckload, for the situation in Question #3. 5) Are radon detectors sold to homeowners accurate? To answer this question, university researchers placed 12 detectors in a chamber that exposed them to 105 picocuries per liter (pCi/l) of radon. The detector readings were as follows:
Use these data to conduct an appropriate hypothesis test. 6) Using the data in Question #5, answer the research question: How accurate are radon detectors sold to homeowners? Discussion question: I pulled the statement of the problem in Computational Exercises #5 from a textbook. They got the data from "real live" researchers on their university campus. Suppose you’re a newspaper reporter, tasked with writing an article on the findings here. What additional information would you like to get from the researchers, to aid you in explaining the relevance of their findings to your readership?
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